Kelvin showed the maximum efficiency with which heat can be converted into work; but there is a dual theorem about the maximum efficiency with which heat at one temperature can be converted into heat at another temperature. It has some surprising implications, in particular that the efficiency with which we heat our buildings could in principle be improved by a large factor. This long known, but still little known, fact is of current pedagogical interest and practical importance.

WTG—Actually, Kelvin had realized it much earlier:
(Lord Kelvin), “On the economy of the heating or cooling of buildings by means of currents of air,” Proc. R. Philos. Soc. (Glasgow) 3, 269–272 (1852).
WTG—There is, however, at least one textbook that presents the principle in terms of Carnot engines: F. H. Crawford, Heat, Thermodynamics, and Statistical Physics (Harcourt, Brace & World, New York, 1963), pp. 217–219.
R. S.
, “
Reflexions sur la puissance chaleurique du feu
J. Heat Recovery Syst.
J. W. Gibbs, “Electrochemical thermodynamics,” Report Brit. Assoc. Adv. Sci. 388 (1886); reprinted in The Scientific Papers of J. Willard Gibbs (Longmans, Green & Co., New York, 1906 and Dover Publications, Inc., New York, 1961), pp. 406–412.
WTG—There is still some loss in the form of the energy required to change the state of whatever was cooked, but the operating cost is zero.
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